9/22/09 KD Big Idea:Observation and description of changes in the world around us are the first steps in finding and learning about patterns.
Essential Question: How can I use graphs, tables and symbols to solve problems?
Notes: The radius is half of the diameter.
A. Copy and complete the table and graph on the previous page to show the relationship between distance and time if the students traveled at the rate of 55 miles per hour.
Time (hours)
Distance
(miles)
0
0
1
55
2
110
3
165
4
220
5
275
6
330
7
385
8
440
B. Use your table and graph to estimate the total distance traveled after: 3 hours: 165 miles 4 ½ hours: About 245 miles 5 1/4 hours: About 288.75 miles
C. If the students continued driving at a steady 55 milesper hour, how far would they go in: 10 hours: 550 miles 12 1/3 hours: 678 miles
15 hours: 825 miles D. Look for patterns in the table and graph that help you calculate the distance traveled at any given time. Write a rule, using words, that explains how to calculate the distance traveled for any given time. The pattern is that you add 55 every time. Once it gets to 2 (or 4,6,8, etc) it becomes (for example with 2) 110 miles. The rule is that you multiply the distance (55miles) by the hour they have been traveling.
E. Use symbols to write your rule from part D as an equation. Hrs x Spd = Dis Example: 8 X 55 = 440 miles
4.1 Follow Up
1. How could you find the distance traveled after 3 1/4 hours by using the table? The graph? The equation? In the equation you do 3.25 multiplied by 55 and you get the answer which is 178.75 miles. Then in the graph I would look between the two whole numbers and estimate what it would be. 2. Estimate how much time it took the students to reach each of the following cities on their route:
a. Richmond, Virginia- about55 milesfrom Williamsburg
b. Baltimore, Maryland- about 3/4 of the way from Williamsburg to Philadelphia
c. Philadelphia, Pennsylvania- about310 milesfrom Williamsburg
A- It took them 1 hour
B- It took them 41 minutes
C- It took them 5 ¾ hours
KD
Big Idea: Observation and description of changes in the world around us are the
first steps in finding and learning about patterns.
Essential Question: How can I use graphs, tables and symbols to solve problems?
Notes:
The radius is half of the diameter.
A. Copy and complete the table and graph on the previous page to show the relationship between distance and time if the students traveled at the rate of 55 miles per hour.
(miles)
B. Use your table and graph to estimate the total distance traveled after:
3 hours: 165 miles
4 ½ hours: About 245 miles
5 1/4 hours: About 288.75 miles
C. If the students continued driving at a steady 55 miles per hour, how far would they go in:
10 hours: 550 miles
12 1/3 hours: 678 miles
15 hours: 825 miles
D. Look for patterns in the table and graph that help you calculate the distance traveled at any given time. Write a rule, using words, that explains how to calculate the distance traveled for any given time.
The pattern is that you add 55 every time. Once it gets to 2 (or 4,6,8, etc) it becomes (for example with 2) 110 miles. The rule is that you multiply the distance (55miles) by the hour they have been traveling.
E. Use symbols to write your rule from part D as an equation.
Hrs x Spd = Dis
Example: 8 X 55 = 440 miles
4.1 Follow Up
1. How could you find the distance traveled after 3 1/4 hours by using the table? The graph? The equation?
In the equation you do 3.25 multiplied by 55 and you get the answer which is 178.75 miles. Then in the graph I would look between the two whole numbers and estimate what it would be.
2. Estimate how much time it took the students to reach each of the following cities on their route:
a. Richmond, Virginia- about 55 miles from Williamsburg
b. Baltimore, Maryland- about 3/4 of the way from Williamsburg to Philadelphia
c. Philadelphia, Pennsylvania- about 310 miles from Williamsburg
A- It took them 1 hour
B- It took them 41 minutes
C- It took them 5 ¾ hours